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 "cells": [
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
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   "source": [
    "import sys\n",
    "import os\n",
    "if not any(path.endswith('textbook') for path in sys.path):\n",
    "    sys.path.append(os.path.abspath('../../..'))\n",
    "from textbook_utils import *          \n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true,
    "tags": [
     "remove-input"
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   },
   "outputs": [],
   "source": [
    "heat_df = pd.read_csv('data/utilities.csv', usecols = ['temp','ccf'])\n",
    "\n",
    "heat_df = heat_df.loc[~(((heat_df['temp'] == 60) & (heat_df['ccf']==129)) | \n",
    "                        ((heat_df['temp'] == 41) & (heat_df['ccf']==16))), :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross-Validation\n",
    "\n",
    "We can use the train-test paradigm to help us choose a model. The idea is to further divide the train set into separate parts where we fit the model on one part and evaluate it on another. This approach is called *cross-validation*.  We describe one version, called $k$*-fold cross-validation*. {numref}`Figure %s <CVDiagram>` shows the idea behind this division of the data.\n",
    "\n",
    "```{figure} figures/CVDiagram.png\n",
    "---\n",
    "name: CVDiagram\n",
    "---\n",
    "\n",
    "An example of fivefold cross-validation in which the train set is divided into five parts that are used in turn to validate models built on the remainder of the data \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cross-validation can help select the general form of a model. By this we mean the degree of the polynomial, the number of features in the model, or a cutoff for a regularization penalty (covered in the next section). The basic steps behind $k$-fold cross-validation are as follows: \n",
    "\n",
    "1. Divide the train set into $k$ parts of roughly the same size; each part is called a *fold*. Use the same technique that was used to create the train and test sets to make the folds. Typically, we divide the data at random.\n",
    "\n",
    "2. Set one fold aside to act as a test set:\n",
    "    + Fit all models on the remainder of the training data (the training data less the particular fold).\n",
    "    + Use the fold you set aside to evaluate all of these models.\n",
    "    \n",
    "3. Repeat this process for a total of $k$ times, where each time you set aside one fold, use the rest of the train set to fit the models, and evaluate them on the fold that was set aside.\n",
    "\n",
    "4. Combine the error in fitting each model across the folds, and choose the model with the smallest error. \n",
    "\n",
    "These fitted models will not have identical coefficients across folds. As an example, when we fit a polynomial of, say, degree 3, we average the MSE across the $k$ folds to get an average MSE for the $k$ fitted polynomials of degree 3. We then compare the MSEs and choose the degree of the polynomial with the lowest MSE.  The actual coefficients for the $x$, $x^2$, and $x^3$ terms in the cubic polynomial are not the same in each of the $k$ fits. Once the polynomial degree is selected, we refit the model using all of the training data and evaluate it on the test set. (We haven't used the test set in any of the earlier steps to select the model.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "NPV2Jr8_A1ES"
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   "source": [
    "Typically, we use 5 or 10 folds.  Another popular choice puts one observation in each fold. This special case is called *leave-one-out cross-validation*. It's popularity stems from the simplicity in adjusting a least squares fit to have one fewer observation. \n",
    "\n",
    "Generally, $k$-fold cross-validation takes some computation time since we typically have to refit each model from scratch for each fold. The `scikit-learn` library provides a convenient [`sklearn.model_selection.KFold`](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html) class to implement $k$-fold cross-validation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To give you an idea of how k-fold cross-validation works, we'll  demonstrate the technique on the gas consumption example. However, this time we'll fit a different type of model. In the original scatter plot of the data, it looks like the points fall along two connected line segments. In cold temperatures, the relationship between gas consumption and temperature looks roughly linear with a negative slope of about $-4$ cubic ft/degree, and in warmer months, the relationship appears nearly flat. So, rather than fitting a polynomial, we can fit a bent line to the data. \n",
    "\n",
    "Let's start by fitting a line with a bend at 65 degrees. To do this, we create a feature that enables the points with temperatures above 65°F to have a different slope. The model is:\n",
    "\n",
    "$$\n",
    "y = \\theta_0 + \\theta_1x + \\theta_2(x-65)^+\n",
    "$$\n",
    "\n",
    "Here, $ (~)^+ $ stands for \"positive part,\" so when $ x $ is less than 65 it evaluates to 0, and when $ x $ is 65 or greater it is just $ x-65 $. We create this new feature and add it to the design matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = heat_df[\"ccf\"]\n",
    "X = heat_df[[\"temp\"]]\n",
    "X[\"temp65p\"] = (X[\"temp\"] - 65) * (X[\"temp\"] >= 65)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we fit the model with these two features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "bend_index = LinearRegression().fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's overlay this fitted \"curve\" on the scatter plot to see how well it captures the shape of the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "hide-input"
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   "outputs": [],
   "source": [
    "temp = np.arange(10, 80, 1)\n",
    "temp65p = (temp - 65) * (temp >= 65)\n",
    "\n",
    "Xs = pd.DataFrame({\"temp\": temp, \"temp65p\": temp65p})\n",
    "y_hats = bend_index.predict(Xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = px.scatter(\n",
    "    heat_df, x=\"temp\", y=\"ccf\",\n",
    "    labels={\"temp\": \"Temperature (<sup>o</sup>F)\", \"ccf\": \"Gas (ft^3)\"},\n",
    "    width=350, height=250\n",
    ")\n",
    "\n",
    "fig.add_trace(go.Scatter(x=Xs[\"temp\"], y=y_hats))\n",
    "\n",
    "fig.update_layout(showlegend=False)\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model appears to fit the data much better than a polynomial. But many bent line models are possible. The line might bend at 55 degrees or 60 degrees, and so on. We can use $k$-fold cross-validation to choose the temperature value at which the line bends. Let's consider models with bends at $ 40, 41, 42, \\ldots, 68, 69 $ degrees. For each of these, we need to create the additional feature to enable the line to bend there: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>temp</th>\n",
       "      <th>ccf</th>\n",
       "      <th>temp40p</th>\n",
       "      <th>temp41p</th>\n",
       "      <th>...</th>\n",
       "      <th>temp66p</th>\n",
       "      <th>temp67p</th>\n",
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       "    temp  ccf  temp40p  temp41p  ...  temp66p  temp67p  temp68p  temp69p\n",
       "0     29  166        0        0  ...        0        0        0        0\n",
       "1     31  179        0        0  ...        0        0        0        0\n",
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     },
     "execution_count": 8,
     "metadata": {},
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    }
   ],
   "source": [
    "bends = np.arange(40, 70, 1)\n",
    "\n",
    "for i in bends:\n",
    "    col = \"temp\" + i.astype(\"str\") + \"p\"\n",
    "    heat_df[col] = (heat_df[\"temp\"] - i) * (heat_df[\"temp\"] >= i)\n",
    "heat_df"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step in cross-validation is to create our train and test sets. Like before, we choose 22 observations at random to be placed in the test set. That leaves 75 for the train set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = heat_df['ccf']\n",
    "X = heat_df.drop(columns=['ccf'])\n",
    "\n",
    "test_size = 22\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X, y, test_size=test_size, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can divide the train set into folds. We use three folds so that we have 25 observations in each fold. For each fold, we fit 30 models, one for each bend in the line. For this step, we divide the data with the `KFold` method in `scikit-learn`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "\n",
    "kf = KFold(n_splits=3, shuffle=True, random_state=42)\n",
    "\n",
    "validation_errors = np.zeros((3, 30))\n",
    "\n",
    "\n",
    "def validate_bend_model(X, y, X_valid, y_valid, bend_index):\n",
    "    model = LinearRegression().fit(X.iloc[:, [0, bend_index]], y)\n",
    "    predictions = model.predict(X_valid.iloc[:, [0, bend_index]])\n",
    "    return mean_squared_error(y_valid, predictions)\n",
    "\n",
    "\n",
    "for fold, (train_idx, valid_idx) in enumerate(kf.split(X_train)):\n",
    "    cv_X_train, cv_X_valid = (X_train.iloc[train_idx, :],\n",
    "                              X_train.iloc[valid_idx, :])\n",
    "    cv_Y_train, cv_Y_valid = (y_train.iloc[train_idx],\n",
    "                              y_train.iloc[valid_idx])\n",
    "\n",
    "    error_bend = [\n",
    "        validate_bend_model(\n",
    "            cv_X_train, cv_Y_train, cv_X_valid, cv_Y_valid, bend_index\n",
    "        )\n",
    "        for bend_index in range(1, 31)\n",
    "    ]\n",
    "\n",
    "    validation_errors[fold][:] = error_bend"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we find the mean validation error across the three folds and plot them against the location of the bend:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "totals = validation_errors.mean(axis=0)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 12,
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tMXLkSCN8x44dQ8+ePc0ScenSpa+SwoEDB6Jdu3bo3bu36RGZNWzatKkRy+RDJx988IFLb8ls44YNG/R6MYPIeyNisGx3JM7HxqFaqUK4q2EZn9QjOxd64cIF5M2b96rDSNm5vXa2TcQlZ86cyJUrl53FBkRZV65cQXx8PPLkyRMQ7bW7kbGxscifP7/dxQZEefJ9QSZiMpqMCQgQCo2Ug7TySw7YepIKFSrk1mM5EhMTE93KaXMmOV08a9Yss69QloEfeeQRtG7dGr169TI16dq1qzlcUrduXbz22muoXr06+vXrZz4LDw9H27ZtsWvXLvODS9Ls2bNdWjB8+HBs3rzZ5pYB6w+fx4PTr5bR1tWKY+oDDW2vS3YuMCYmxpxgTx4D2bmtdrdN/n3myJHD429QdtfXn8q7fPmyefsCxUWn16Kjo81kgYxfJu8SkP+Iy38Uc+fO7d3AjGb+oyjfGzJ6K0tGmNz9fuJYKZTGyRJVkyZNjNDJLGF6aezYsYiMjMSJEycwevRok2X16tUYOnSoY/cUvjBnC77667BLc+Y+1QaNKxXl8PcSAS4fewlkOmG4fKzHlsvHemwlsmwvCgkJoRQqYObysQLUf0IG5PKx7CUsWrQoSpUqBfkfx+eff45x48aZ08Vp7Tj1nsK9e/eaGcSFCxeiTJkyZvm5SpUqRgwzSr7aU/jIZ+uwdMdJl6pNfagZOtUprTeqAiwypVCvwymFemwphXpsKYW6bCmFenwDUgoXLFhg9hDKPjABIPsEH3jgAbRo0cKFtEihLC+L/EmSk8jjx483f5bZxQkTJqBIkSKOlMKR32/F56sPudTtodZV8Eq3enqjKsAiUwr1OpxSqMeWUqjHllKoy5ZSqMc3IKVQcMpGSvmBI5sirW5W9ZcbTcKOnkfvD//ExfgElxHUrWE5DOpYEzVKFdQbXQESmVKo19GUQj22lEI9tpRCXbaUQj2+ASuFekhdI/tq+VhqcvzcBfyy7QROR8WgTsUQFMufG099sQFnYi4ZIRzYoQa6Ny5vJ45sVxalUK9LKYV6bCmFemwphbpsKYV6fCmFemxTIvtSCqUScppIfrgWL17c1Cn2UgL+810YFoQdN38f0K4ahtxSG8G5kk5QM1kjQCm0xstKbkqhFVrW8lIKrfGympsHTawScz8/pdB9VlZzUgqtEvMgv9OkMLkJX645jBFzt5i/3lCzJAZ3qoUmlYt50MLAfoRSqNf/lEI9tpRCPbYSmVKox5dSqMeWUqjHNiWyU6VQKrj12HkMmx2GbcejUKJAsNlnKAdRmNwnQCl0n5XVnJRCq8Tcz08pdJ+VJzkphZ5Qc+8ZSqF7nDzJRSn0hJrFZ5wshdIUea34az/uwMcr9puW3d20AoZ1DkXJgrzpwJ2uphS6Q8mzPJRCz7i58xSl0B1KnuehFHrOLrMnKYWZEfL8c0qh5+zcftLpUpjckB82HcewOWG4cCkB9coVxpBba6ND7VJutzNQM1IK9XqeUqjHllKox1YiUwr1+FIK9dhSCvXYpkT2FymUCu+LiDazhkt3nILczjT45lp45qaaNlDy3yIohXp9RynUY0sp1GNLKdRlSynU40sp1GPrl1KYXOkJv+zGpF/2mL+2qlYCuYNy4MiZCyiQJwi31itj9h4yJRGgFOqNBEqhHltKoR5bSqEuW0qhHl9KoR5bv5ZCqfyS7Sfx+o87sP90jAulkbfXwaNtq9lAz/lFUAr1+ohSqMeWUqjHllKoy5ZSqMeXUqjH1u+lUBogdyfLHcppU7uaIZjxiOu1gDbgdFwRlEK9LqEU6rGlFOqxpRTqsqUU6vGlFOqxzRZSuO7gWfT6YJULpZqlCmLJ4PY20HN+EZRCvT6iFOqxpRTqsaUU6rKlFOrxpRTqsc0WUnj+QjwavrI4XUoPtqqMZzvVDPhX11AK9f4RUQr12FIK9dhSCnXZUgr1+FIK9dhmCymURsxcfQhvLNqJmLjLpk1VShZAxN9x5u/VQwri2Y410a1RORtIOrMISqFev1AK9dhSCvXYUgp12VIK9fhSCvXYZhsplIbIC64PRsYgf3AQShfOi+3Ho/Dur3uwaGu4aWef5hXxbKdaKFskrw1EnVUEpVCvPyiFemwphXpsKYW6bCmFenwphXpss5UUXgvTF2sOGzkMP38RlYrnN8vJPZtUsIGqc4qgFOr1BaVQjy2lUI8tpVCXLaVQjy+lUI9tQEihNPLwmVi8u3QPvl1/1LRZpFDkUCQxEBKlUK+XKYV6bCmFemwphbpsKYV6fCmFemwDRgqTGzpv03Eza7j3VLRZRpblZFlWzu6JUqjXw5RCPbaUQj22lEJdtpRCPb6UQj22ASeF0uAzMZeMGH668qBpvxxAkYMociAluyZKoV7PUgr12FIK9dhSCnXZUgr1+FIK9dgGpBQmN3rpzlNmSXnTkXPmlTWynNyyanGs2HMaF+ITUCOkIG6rX8YG+vpFUAr1GFMK9dhSCvXYUgp12VIK9fhSCvXYBrQUSuMvXb5iZg3f/XVvupTvalweE+5pZEMP6BZBKdTjSynUY0sp1GNLKdRlSynU40sp1GMb8FKYDOCvA2fw1BcbcDo6zoX28v908PsDKZRCvX9ElEI9tpRCPbaUQl22lEI9vpRCPbaUwlRs73p/JTYePudCe86TrdGkcjEbekGvCEqhHltKoR5bSqEeW0qhLltKoR5fSqEeW0phKrZPfL4eP/3zouvUyO9rUQnDO4eicL7cNvSEThGUQh2uEpVSqMeWUqjHllKoy5ZSqMeXUqjHllKYiu2vO0+h//S1V9EukCcIMXEJqF26EJ7qUB13NipvQ294vwhKofeZJkekFOqxpRTqsaUU6rKlFOrxpRTqsaUUpmG77XgUVuyJwIVLCahRqiBaVi2Bycv24rNVSa+vESkUORRJ9KdEKdTrLUqhHltKoR5bSqEuW0qhHl9KoR5bSqGbbH/beQqTf9uLdYfOmmXkp26sjifaV3fzad9noxTq9QGlUI8tpVCPLaVQly2lUI8vpVCPLaXQIlt5dY3I4cX4BPNOw6c61ED7WiEWo9ifnVKox5xSqMeWUqjHllKoy5ZSqMeXUqjHllLoAdstx84bMUw+lNKvdRUzc1iqcF4PotnzCKVQjzOlUI8tpVCPLaVQly2lUI8vpVCPLaUwC2xn/XUYk3/bhyNnY1G5RH48eWMNx96jTCnMQkdn8iilUI8tpVCPLaVQly2lUI8vpVCPLaUwi2xPRl00t6F8vvqQiXRrvTK4/bqy+GPPaeyPiDb7Dzs3KIu7m1bIYklZe5xSmDV+GT1NKdRjSynUY0sp1GVLKdTjSynUY0sp9BLbX3acNEvK8vLrHAAS08R9997GuKNhOS+VZj0MpdA6M3efoBS6S8p6PkqhdWZWnjh16hRCQkKQI4d812LyJgFKoTdpXh2LUqjHllLoZbb/981mzN5w1CWqr+9QphR6uaNThaMU6rGlFOqx5UyhLltKoR5fSqEeW0qhl9n+sv0kHp2xziXqDTVL4vNHWnq5NPfDUQrdZ2U1J6XQKjH381MK3WflSU7OFHpCzb1nKIXucfIkF6XQE2oWn6lZsyb27Nlj8SnvZY+PjzfXhRUvXtx7QX0QaV9ENDq+/btLyXIzytBbQyEnlX2RKIV61CmFemwphXpsOVOoy5ZSqMeXUqjHljOFCmzH/bQT7y/blxI5pFAeRPwdZ/4u7zSUdxvKOw7tTJRCPdqUQj22lEI9tpRCXbaUQj2+AS2FCQkJkG+M+fLlcyEcFxeHnDlzInfu3C6fyXMCrkCBAm71DGcK3cLkdiY5lXzkTCwK5s2N0DKFsGT7Sbz3615sPnrOxJDbUOTdhnI62Y5EKdSjTCnUY0sp1GNLKdRlSynU4xuQUnjw4EGMGTMG69Yl7U+rX78+hg0bhgYNGmDnzp3ms61bt5rPbr31Vrz88ssp4jh58mRMnDjRCGHz5s1T/pxRF1EK9QZw6sjjl+w2p5QTriSa+5PlHmW5T1k7UQr1CFMK9dhSCvXYUgp12VIK9fgGpBRGRERgzZo16Ny5syE7ZcoUbNq0CVOnTkVYWBiOHDmCLl26IDY2Fo888gh69+6NHj16mM8GDBiAefPmoWTJkhgyZAgqVqyIwYMHZ9hDlEK9AZw2ctjR85i0dDeW7jhlPhIpFDkUSdRKlEItsjB7YYOCgpA/f369QgI0MqVQt+N50ESPL6VQj21ASmFanHPnzsW0adMwf/58F9LvvPOO+cH04osvYtKkSYiKisKoUaNMvvXr1+O5557DihUrKIV6Y9SjyPLCa1lSDo+6aJaRZTlZlpU1EqVQg2pSTEqhHltKoR5biUwp1ONLKdRjG7BSKA3fvXu3mSGcPn06Bg0ahO7du19FOjExEXfddReefvpp3HzzzRgxYgRCQ0PRt29fk0/+0bdp08YsOctsxrUSZwr1BnBGkWXv4YQluzFr7RGTTQ6gyEEUOZDizUQp9CbNq2NRCvXYUgr12FIKddlSCvX4BqwUHjhwwIigCF3Lli0xcuRII3yp04cffmhmAUUac+XKhYEDB6Jdu3ZmOVmSzBo2bdrUiGXyoZNXXnnFpbc+//xzrF27Vq8XM4kscnv58uV0D834rFI2Frxszxl8uPIIdoRHm1LvbVoWvRqXwaEzFxCfkIjqJfOjRojny5Pyw1UOJPHmAu93qoxb4ZrRf7q8X2pgRLxy5Qrk0Fx6h+kCg4BuK+WwYp48eXQLCdDo8n1BDoLKLybvEpDvC/JLnMeTVLRoUbcey5EoZuLAJP9wZ82aZfYVrly5MuWHz8KFC/HGG2/g+++/R4kSJUzNZdm4evXq6Nevn/l7eHg42rZti127dqUMzj/++MOllQ8//HDKwRVfIJB/QBcuXEChQnr76nzRLqtlTvp1H6YsPwAZiXLzVOoROahDNTx9YzWrIU1++c9BwYIF+Q3KI3oZPyTjVr7x84er9+HK9wWZFZCxy+R9AjKbVbhwYf5n0ftoERMTY/4zExwcrBA9sEPKJIe829jdt6ukpeXu92rHSqE0SJaomjRpgkWLFqFGjRr4/fffzWnkzz77DLVr105ps4jjiRMnMHr0aPO11atXY+jQodxT6Ef/huQgysOf/oXImEsutd7x6m3Il/va2wCu1UwuH+sNAC4f67Hl8rEeW4nMPYV6fLl8rMc2IJePZS+hTHGWKlXKzKDJ8u64cePM6eJt27bh0UcfxSeffIJ69eqlkM+bNy/27t2LXr16QWYRy5QpY5afq1SpYsQwo8Q9hXoD2JPIHd5ahgOnY1we/enZdggta302lVLoSS+49wyl0D1OnuSiFHpCzf1nKIXus7Kak1JolZj7+QNSChcsWGD2EIroCQDZJ/jAAw+gRYsWeOyxx7Bs2TIXgiKLMlU9Y8YMjB8/3nwus4sTJkxAkSJFKIXujzmf57zr/ZXYeDjpRdepU72yhTGoU03cWq+MpTpSCi3hspSZUmgJl6XMlEJLuCxnphRaRub2A5RCt1FZzhiQUiiUZIO1/MCRfXZWN7HzRhPL48xRD0xfdRAv/7DtqjoVzpsbURfjzdf6NK+IJ2+sgcol3Dt8QinU615KoR5bSqEeW4lMKdTjSynUYxuwUqiH1DUyl4/tpO1eWfPDjmPlntOIu3wFdcsVxmNtq+Htxbvx7q97TIBShfPgqRtroF/rKpkGpBRmisjjDJRCj9Fl+iClMFNEWcpAKcwSvgwfphTqsaUU6rFNiUwptAGyl4qQgyhvL96F33dHmIjyTkN5t6G84/BaiVLoJfjphKEU6rGlFOqx5UyhLltKoR5fSqEeW0qhDWy1ipAbUSb8shuR0UmnlOU2FLkVRW5HSZsohVq9wBtN9MgClEJNulw+1qRLKdSjSynUY0sptIGtZhFyI4osKX+zLulGFLk/We5RlvuUUydKoV4vcKZQjy2lUI8tZwp12VIK9fhSCvXYUgptYGtHEUu2nzRLyjvD/zbFiRSKHIokSqLm4Y14AAAgAElEQVQU6vUCpVCPLaVQjy2lUJctpVCPL6VQjy2l0Aa2dhaR+iCKLCPfWq80ws/H4WDE3yhZKC96NK2AB1tVtrNK2b4sSqFeF1MK9dhSCnXZUgr1+FIK9dhSCm1ga3cRaQ+ipC3/477NcHPd0nZXK9uWRynU61pKoR5bSqEuW0qhHl9KoR5bSqENbH1VxNDvNuPbdUddipdX2Lzc7d+bcHxVv+xSLqVQrycphXpsKYW6bCmFenwphXpsKYU2sPVVEd+uO4Kh34W5FH9fy0p47a4GvqpWtiuXUqjXpZRCPbaUQl22lEI9vpRCPbaUQhvY+qqIsKPn0O29lS7F92hSAeN7N/RVtbJduZRCvS6lFOqxpRTqsqUU6vGlFOqxpRTawNaXRciJ5Hd/3etShQ8ebIrbLN6f7Mt2OLlsSqFe71AK9dhSCnXZUgr1+FIK9dhSCm1g6+siLsQnYPvBE6hUugRG/bAdP20NR55cOTGtX3O0qVHS19Xz+/IphXpdSCnUY0sp1GVLKdTjSynUY0sptIGtE4pIfk9hQmIOPDTtL/y5PxIlC+bBl4+1RK1/3mXohHr6Yx0ohXq9RinUY0sp1GVLKdTjSynUY0sptIGtE4pI/fLq4+cu4JHP1mHHiShUKVkAPwxsg8J5Xa/Gc0K9/aEOlEK9XqIU6rGlFOqypRTq8aUU6rGlFNrA1glFpL3RRIRQxFAEsUH5Ipj/zA1OqKZf1oFSqNdtlEI9tpRCXbaUQj2+lEI9tpRCG9g6oYj0rrlbvT/SiGFM3GVcX70EvnqslROq6nd1oBTqdRmlUI8tpVCXLaVQjy+lUI8tpdAGtk4o4lp3H/+0LRxPzFxvqii3nMhtJ0zWCFAKrfGykptSaIWW9bynTp1CSEgIcuTIYf1hPpEhAUqh3gChFOqxpRTawNYJRVxLCqVuX689gmGzk15y3aNJeYzv3cgJVfabOlAK9bqKUqjHljOFumwphXp8KYV6bCmFNrB1QhEZSaHU76Pl+/HajztMVR9qXQWv8Bo8t7uNUug2KssZKYWWkVl6gDOFlnBZykwptITLUmZKoSVcnmWuWbMm9uzZ49nDXngqPj4e8sO1ePHiXojGEGkJZCaFkv9/P+/C5N+SXnQ9vHMonmhfnSDdIEApdAOSh1kohR6Cc/MxSqGboDzIRin0AJqbj1AK3QSVlWyUwqzQc/6z7kihtOLFuVvxxZpDpkET72mE7o3LO79xPq4hpVCvAyiFemwlMqVQjy+lUI8tpVCPbUpkSqENkH1YhLtSKFUc+OUGLAg7YWo7a0ArtKpWwoc1d37RlEK9PqIU6rGlFOqypRTq8aUU6rGlFNrA1glFWJFCqe+Dn6zBij2nTdWXDb0RVUoUcEIzHFkHSqFet1AK9dhSCnXZUgr1+FIK9dhSCm1g64QirEqh1PmO9/7AlqPnTfV3vnob8uYOckJTHFcHSqFel1AK9dhSCnXZUgr1+FIK9dhSCm1g64QiPJHCmEuX0XniChw+E4vcQTlxXYUiuHwlEU0qFcWQW2qjQJ5cTmiaz+tAKdTrAkqhHltKoS5bSqEeX0qhHltKoQ1snVCEJ1Io9T4UGYubJ/yOS5evXNUMvuj6XxyUQr0RTinUY0sp1GVLKdTjSynUY0sptIGtE4rwVAql7k3HLEFk9CWXZmwffRvyB3NJmVKoN8IphXpsKYW6bCmFenwphXpsKYU2sHVCEVmRwkajF+NcbLxLMzaOuhnFCgQ7oXk+rQOlUA8/pVCPLaVQly2lUI8vpVCPLaXQBrZOKCIrUnj/1DVYuTfpJHJyKpQ3F7a8fKsTmubzOlAK9bqAUqjHllKoy5ZSqMeXUqjHllJoA1snFJEVKVx36Cye/3oTjpyJvaop/+1aF/1vqOqE5vm0DpRCPfyUQj22lEJdtpRCPb6UQj22lEIb2DqhiKxIYXL9d4b/jYQrifh67RHM+POg+fL79zdBlwZlndBEn9WBUqiHnlKox5ZSqMuWUqjHl1Kox5ZSaANbJxThDSlM3Y7nvt6E7zceM1+a81RrNKlUzAnN9EkdKIV62CmFemwphbpsKYV6fCmFemwphTawdUIR3pZCadPDn67Fb7tOmeatGn4TyhXN54Sm2l4HSqEeckqhHltKoS5bSqEeX0qhHltKoQ1snVCEhhRKu+56fxU2Hj5rmrj/9S7ImSOHE5prax0ohXq4KYV6bCmFumwphXp8KYV6bCmFNrB1QhFaUihtu+ntZdgfEYMCwbmwbXTgnUimFOqNcEqhHltKoS5bSqEe34CWwoSEBMg3xnz5XJfm5DOBU6BAARf6GX2WXlfVrFkTe/bs0evFTCLHx8dDfrgWL17cZ3XIzgVrSqFwa/rqEkTGXEL1kIJY+n/tszNKl7ZRCvW6m1Kox5ZSqMuWUqjHNyCl8ODBgxgzZgzWrVtnyNavXx/Dhg1DgwYNzN8nT56MiRMnGiFs3rx5yp8z++xa3UQp1BvAToisLYXnL8QbMZS7kdvUKIkvHm3phGbbUgdKoR5mSqEeW0qhLltKoR7fgJTCiIgIrFmzBp07dzZkp0yZgk2bNmHq1KkICwvDgAEDMG/ePJQsWRJDhgxBxYoVMXjw4Aw/y6iLKIV6A9gJkbWlUNq4LyIaHd/+3TS3Z9MKePvuhk5ounodKIV6iCmFemwphbpsKYV6fANSCtPinDt3LqZNm4b58+dj0qRJiIqKwqhRo0y29evX47nnnsOKFSsy/IxSqDdInR7ZDikUBmsOnME9H/5pcDzdoQaG3lrb6WiyXD9KYZYRXjMApVCPLaVQly2lUI9vwEqhNHz37t1mhnD69OkYNGgQunfvjhEjRiA0NBR9+/Y11E+dOoU2bdpg586dRhSv9VlQUNA1e4kzhXoD2AmR7ZJCaevCLSfw9BcbTLPHdK+PB1pVdgICtTpQCtXQmv3UMTExKFYscN+DqUc36WdHSEgIcgTgWwM0uUpsSqEe4YCVwgMHDhgRFNlr2bIlRo4caYRv4MCBaNeuHXr37m2oy6xh06ZNjTzKvsNrfZZ8IOWpp55y6a0lS5aY5WpfpcTERMjhmFy5cvmqCtm63MuXL0P+U2DXN/+vN4TjzV8OGKYTeoSifY3s+0Ndxq1wzZkzZ7YeQ75o3JUrVyC/+H1Bh74c8BO2dn1f0GmFM6Py+4Jev8j3BHGGjCa6Mird3QOtORKlFAemuLg4zJo1y+wrXLlyJV5++WVUr14d/fr1M7UNDw9H27ZtsWvXLrz00kvX/Cz5h1Z6p4y7dOmC7du3+6z1Ii2xsbEoXLiwz+qQnQs+d+6cYWunuExcuheTl+03WL9/shXqlcuefSvjVrjmzZs3Ow8hn7RNvi9cuHABhQoV8kn52b3Qs2fPchZWqZOjo6MRHBxsfjF5l4CsIMivggULehQ4d+7cbj3nWCmU2ssSVZMmTbBo0SLIrN6JEycwevRo07DVq1dj6NChZk+hiOO1PsuIApeP3RojfpvJzuXj1JBemLMFX/112Hxp3chOKFkwj98yvFbFuXys16VcPtZjK5G5fKzHl8vHemwDcvlY9hIWLVoUpUqVMv9T/vzzzzFu3DhzuvjYsWPo1asXFi5ciDJlypgl5ipVqhgx3Lt37zU/oxTqDVKnR/aVFAqXATPWYfH2kwaR3JN8KioOJQoGo3mV7PFOSkqh3uinFOqxpRTqsqUU6vENSClcsGCB2UMoS1ICQPYJPvDAA2jRooUhPWPGDIwfP978WWYQJ0yYgCJFimT62bW6iTOFegPYCZF9KYXS/h7vr8KGf67DS+bRunoJfPlYKyfgyVIdKIVZwpfhw5RCPbaUQl22lEI9vgEphYJTNqrKDxzZT5PehkreaKI36LJbZF9L4Y9bTuCpf04kp2b7Zs/rcE/zin6Nm1Ko132UQj22lEJdtpRCPb4BK4V6SF0jc6bQTtr2l+VrKfzg9314Y9FOl4Y/dWN1/Oe2UPuBeLFESqEXYaYJRSnUY0sp1GVLKdTjSynUY5sSmVJoA2QfFuFrKfxizWG8OHeLC4HhnUPxRPvqPiST9aIphVlneK0IlEI9tpRCXbaUQj2+PpNCeWnqXXfdha+++golSpQwLZRbRVq1aoW6deuav0dGRuLee+/F7Nmz/fq1CZRCvQHshMi+lsLw8xfRcfzviIm7fBWOm0JLYVq/5k5A5HEdKIUeo8v0QUphpoiylIGnj7OEL8OHKYWueM5fiMeRM7EomDcXqpQo4DF8n0mhdGqzZs3MuwHlFLAkuVHk8ccfT7mTOPk2kXXr1qUc9PC4pT58kFLoQ/g2FO1rKZQmbj8ehW/WH4EIYtF8wZi1NulVNX1aVMIbPRrYQEGnCEqhDleJSinUYyuRKYV6fCmFV7N9Z+kejF+yO+WLctBw6kPNkD/Y+oUVlEK9cZsSmVJoA2QfFuEEKUzb/MjoS2g6Zon5cv82VfHfO5Jm3/0tUQr1eoxSqMeWUqjLllL4L99DkbFo/7/fXIA/c1NN/N8ttSx3BKXQMjLrD1AKrTPzpyecKIXC78T5i7j+9aUG5dMdamDorbX9CaupK6VQr8sohXpsKYW6bCmF//L9decp9J++1gX4zXVL4+O+zSx3hM+l8Pnnnzcvkpb0zjvvoH379mjYsKH5u1wfJu8I5PKx5X696gG5g1N+uLp7J2HWSgu8p50qhdITByNjcOP/lplOESkUOfSnRCnU6y1KoR5bSqEuW0rhv3xX7j2N+6eucQHerWE5vHNvY8sd4TMplLsLu3Xr5laF582bx4MmbpFKPxOlMAvw3HjUyVIo1d998m/cMmG5aYksI8tysr8kSqFeT1EK9dhSCnXZUgr/5ZtwJRH1XvoZF+MTroL+du+G6NmkguWO8JkUWq6pHz/A5WM/7jw3qu50KZQmbD12Hl3f/cO0ZvSd9dD3+iputMz3WSiFen1AKdRjSynUZUsp/Jfv9JUH8fL8bcgdlAPVQgqieP5gdGlQFg9eX9mjTnCkFF65cgUREREICQlBzpw5PWqYkx6iFDqpN7xfF3+QQmn1hkNn0WPKKgNgTPf6eKCVZ980vE/w2hEphXq0KYV6bCmFumwphUl8txw9jye/WI+jZy9gXK/r0LtZ1m+w8qkUDhs2DLfffru5ezg5yVLxW2+9hfDwcPP+wunTpyM01L9vZaAU6n6D8HV0f5FC4fTn/kjc+9Fqg+y1uxrgvpaVfI0vw/IphXrdQynUY0sp1GVLKUzi++ysTZi36Rg61y+DKQ809Qp0n0mhzAY2adIE7733Hm644QbTmKNHj6JDhw548MEH0alTJ3z00UcoVqyYOWziz4lS6M+9l3nd/UkKpTW/747AQ9P+Mg17o+d16OPg+5EphZmPP09zUAo9Jefec3xPoXucPMlFKQRm/HkI/523FQXy5MKS59uhXNF8nqB0ecZnUnj48GF07NgRa9asSTkVO27cOPz0009YsmQJgoKCsH37dtx3331Yv369+bu/Jkqhv/ace/X2NymUVi3ZfhKPzVhnGuitZQf3aFnLRSm0xstKbkqhFVrW81IKrTNz94lAl8Jtx6Pw+Mx1Ztl47F31cX9L720F8pkUJt9o8ssvv6By5cqQ08gyYzh8+HD06dPHjI2EhASzdPzjjz9CxMpfE6XQX3vOvXr7oxRKyxaEncDALzeYRr51d0P0amr9pJp7hDzPRSn0nF1mT1IKMyOUtc8phVnjl9HTgS6Fg7/ZjDkbjqJjndL45CHr7yLMiK3PpFAq1bdvXxQoUMAsF3/xxRfYv38/5s+fj1y5kq5mOXv2LFq0aIHffvsNFSo47weWu0OeUuguKf/M569SKLTnbDiGwd9sMuDH926EHk3KO6oTKIV63UEp1GMrkSmFenwDWQq/WHMYL87dgvzBQVj0bDtULpHfq6B9KoV//fUXBgwYgJiYGDRq1AijRo3Cddddl9LApUuX4oknnjDLyLlz5/Zqw+0MRim0k7b9ZfmzFAqtWX8dxvA5Wwy452+uhSL5kv6tNapY1PzyZaIU6tGnFOqxpRTqsg1UKdwZ/jce/WytWTZ+6Y56eLiN918t5lMplGEjS8SydFykSBGXUXT8+HEzW1ivXj3dEaYcnVKoDNjH4f1dCgXfZ38exEvztrmQHNW1Lh65wXcvu6YU6g1uSqEeW0qhLttAlcIh327Gd+uPokPtUvj04eYqkH0uhSqtclhQSqHDOsTL1ckOUihIGr6yGOcvxF9Fp3zRfFg5/CYvE3M/HKXQfVZWc1IKrRKzlp/Lx9Z4WckdiFI4a+0RDJ8dhry5g7DgmRtQo1RBK8jczuszKZRv9m3btnWrosuXL0fhwoXdyuvETJRCJ/aK9+qUHaQwPuEKar64KF0oe8Z2Ru4g37xEnlLovXGaNhKlUI8tZwp12QaaFO45FY2HP/3LLBuP6FIHA9pVUwPsMymMiopC06ZJL1u84447zMnj5AMmaVvbuXNn7inMwhDg3cdZgOfGo9lBCqWZzcf8gojouKtaXKJgMNaPvNkNCjpZKIU6XCUqpVCPLaVQl22gSWHysnH7WiH4rH8LVbg+k0Jp1d69ezF37lxz8jhv3rzmVTTdu3dHlSre3zypSjGT4Jwp9CV9/bKzixRO/GU3Jv6y5ypg9coVwcJBSS+X90WiFOpRpxTqsaUU6rINJCn8dt1RDP1uM4Jz5cT3T7dB3bK6q6Y+lcLkYSMzWfLamW+//RbLli1Ds2bNjCDecsstyJfPO2/p1h2iGUenFPqSvn7Z2UUKhZS81Hrj4bM4GxuPn7eF40zMJYy8vQ4ebau3XJFRD1EK9cYvpVCPLaVQl22gSOH+iBj0nbbGLBv/57ZQPHVjdV2wABwhhalbeeLECcj9xzJ7KPcf33///RgxYgSCg4PVYWgVQCnUIuuMuNlJClMT/XHLCTz1RdLLrWf0b4F2tUJsB04p1ENOKdRjSynUZRsoUpi8bNy2ZghmPqK7bJzcY46TQnlFzcqVK/HNN9/g559/RokSJSDvK5SXXPtrohT6a8+5V+/sKoXSellOlmXlWqULGTEsUySve1C8lItS6CWQ6YShFOqxpRTqsg0EKZRXz4gUyiG/7568Hg0r2PPOWMdI4aFDh8wM4ZdffonIyEh06dIFPXv2RJs2bfz63mP5p0Ep1P0G4evo2VkKha3MFsqsYdfryuK9+5rYiptSqIebUqjHllKoyza7S+GhyFjcP3W1WTYecmttDOxQQxdoqug+lcILFy5g8eLFZi/hmjVrzD3H99xzD26//XYUK1bMNgjaBVEKtQn7Nn52l8Lj5y6g77S/sPdUNAbfXAuDOtp3DzmlUG9sUwr12FIKddlmdylMXja+oUZJfP5oS12YaaL7TAqTr7aT+tx5553o2rXrNW8uKVmyJHLkyGErGG8WRin0Jk3nxcruUijEl+2KQL9P/zLwP3igKW6rX8aWjqAU6mGmFOqxpRTqss3OUpi8bByUMwe+HnA9mlWxd4LMZ1IonSqnjN1J69atS/caPHeedUIeSqETekGvDoEghULvo+X78dqPO1ChWD7M6N8S1UL09/lSCvXGLaVQjy2lUJdtdpVCWS7u89GfZtn4/26phWdusm9VJrnHfCaFiYmJOHnypFsjp3Tp0pwpdItU+pn48uoswHPj0UCRQkGRvKxxU2gpTOunc/dmauSUQjcGoIdZKIUegnPzMV5z5yYoD7JlRymMu3wFL87dYu42bl29BL58rJUHZLL+iM+kMOtV958InCn0n77ypKaBJIXnYuPNe7PCjp7HE+2rY3jnUE+Quf0MpdBtVJYzUgotI7P0AKXQEi5LmbOTFP7fN5sxP+w4Ll2+YhjIVrmvB7RCi6rFLTHxVmZKobdIZhCHUmgDZB8WEUhSKJj/OnDGHDy5GJ+A8b0boUeT8mr0KYVqaHnNnR5aE5lSqAc4u0jh24t3491fr75FSm4u2fLyrciTyzf3zVMK9cZtSmRKoQ2QfVhEoEmhoP589SGM/H4rihcIxoxHWqB+uSIqPUApVMFqgnKmUI8tpVCXbXaRwns/Xo0/90W6wJrzZGs0qWzvAZPkSlAKdceuiU4ptAGyD4sIRCkU3P+dtxUz/jyEVtVKGDEMDvL+/2wphXoDm1Kox5ZSqMs2u0jhPR/+iTUHzrhK4VOt0aQSpVB3FPkwOqXQh/BtKDpQpVD2wMgy8ur9kXjo+ip45c56XqdNKfQ60pSAlEI9tpRCXbbZQQpPRcWhx5RVOHo29ipYRfPlxrqRNyNXkG9ew8eZQt2xy5lCG/j6uohAlULhvvXYeTw47S+cjbmEsd3r4/5Wlb3aHZRCr+K8KhilUI8tpVCXrb9LodxY8sxXGxF29Bzy5Q5Czpw5EHc5AXXLFsZznWpB3u7gqxTQUij3LMs3xnz58rnwv3Llivksb17Xu17lOQHn7n3MnCn01fC2p9xAlkIhPHvDUcgJOvnmJsvIzat479QcpVBvDFMK9dhSCnXZ+rMU7gz/2wjhnpN/o2rJAnjn3sZoUF5nT7YnvRCQUnj27FmMGzcOixYtMszkJdovvPACqlevbv7+5ptvYsGCBZD3+9WtWxdjxoxBuXLlzGeTJ0/GxIkTjRA2b9485c8ZwacUejI0/eeZQJdC6anXF+3Eh7/vM5e2ixgWyZfbKx1IKfQKxnSDUAr12FIKddn6qxRuPHwOg77aiCNnY1G/fBG806exLZcAWOmNgJTCc+fOYfbs2bjvvvsQHBxsBFG+JjK4efNmPP7441i6dKmZQRw7diyCgoIwYsQIhIWFYcCAAZg3bx7k6r0hQ4agYsWKGDx4cIbMKYVWhqT/5aUUJvXZw9PX4redp3B30wr4390NvdKRlEKvYKQU6mG8ZmS+kkYPuj9K4ap9kUYIT0fHmcN5k/o0QunCriuRetTcixyQUpgWzapVq/Dqq6+amUP588svv4yffvoJOXPmxPvvv48TJ06YzydNmoSoqCiMGjXKhFi/fj2ee+45rFixglLo3njLlrkohUndui8i2hw8OXb2Au5sVM78T7hM4by4o2HSLLsniVLoCTX3nuFMoXucPM1FKfSUXObP+ZsULt1xCoNmbURM3GV0DC2FSfc2RsE8uTJvqA9yUAoBM1N4+fJlMxsYFxeHxx57DLKnUJaVf/jhB3zyySeoWrWq+Tw0NBR9+/Y1XSX/6Nu0aYOdO3ea2cRrJc4U+mBk21gkpfBf2HM2HMPgbzZdRb9hxaKY93Qbj3qEUugRNrceohS6hcnjTJRCj9Fl+qA/SeGCsBNmhvBKYiK6NSxnhNA354ozxWoyBLwUrl27Fs888wy+//57lClTxkCZM2cOhg0bZv7cvXt3s6cwT548GDhwINq1a4fevXubz2TWsGnTpti0aVPKoZNevXq5kJclaZmB9FWSe6bll8x8MnmfgPwHgmyTuH698STe+vWQC+RXu1THbXVKWIYv41aSXP3E5F0C/L7gXZ5po/H7gh5ff/m+MH/raYz+eb8Bcdd1IRhxc1U9KF6KnFW2ISEhbtUkR2JySW5ltyfTvn370LNnT0ydOtXMCkr67bffzFLxp59+avYUylJx/vz5MWHCBPNnOYzSr18/kzc8PBxt27bFrl27UqRA/geTNklsyeOrJLOg0dHRKFq0qK+qkK3LPXPmDIoUKZLhbHG2BpCqcW/8tAsfLU/6Jpg6Db+tNga0q2YZg4xbmYVP7w0BloPxgasIyEG62NhYM3aZvE9AVhBKlCjB/9B4H62ZkJGJGvnl1DRz9SG89MN2U71HbqiKF7vo3hPvLQ6yWiq/Chcu7FFIdydIHCeFx44dM0IoS8LdunVLafzIkSNRtmxZPP300+Zre/bsQZcuXcwS8UcffWT2F44ePdp8tnr1agwdOpR7Cj0aOtnnIS4f/9uXH6/Yj7ELd7h07lt3N0SvphUsdzqXjy0jc/sBLh+7jcqjjFw+9gibWw85ffn4w+X78fqPSd8Hn+1UE893quVWu5yQKSCXj+Ufa58+fdC/f3+kXu6Vk8jz58/Ht99+i48//ticTP7ss8+wZs0afPjhh9i7d6/Jv3DhQrPUPGjQIFSpUsWIYUaJewqdMNT16kAp/JftifMX0fWdFYiMuXQV8Il9GqN7I+sHTiiFeuOWUqjHViJTCvX4OlkKJ/6yBxN/2W0aP6JLHY9WSPTIZR45IKVw2rRpeP31113ozJw5E40aNcIrr7xilpElNWjQAM8//7x5X6GkGTNmYPz48ebPTZo0McvKmS2/UAozH4j+nINSeHXvHT93AfPDTuD033E4GBmDJdtPonyxfJjRvwWqhxS01NWUQku4LGWmFFrCZTkzpdAyMrcfcKoUJr+vVRoy9q4GuL9lJbfb5JSMASmF7sCXTcKyrp7eXibeaOIOwcDJQynMuK+HfrsZ364/ig6hpfBpv+aWBgal0BIuS5kphZZwWc5MKbSMzO0HnCKFe05FY39EtLnNafH2k/h8ddIhO3kH4Z2NyrvdHidlpBTa0BucKbQBsg+LoBRmDP/8hXj0/eQvbD56Do+3r44XOru/4ZpSqDewKYV6bCUypVCPrxOkcNxPu/D+sr0ujZzatxk61S2t13jlyJRCZcASnlJoA2QfFkEpzBz+2oNnjBheiE/A270bomcT9w6dUAozZ+tpDkqhp+Tce45S6B4nT3L5WgpP/R2HFmN/cal6u5oh5ppPf06UQht6j1JoA2QfFkEpdA/+F6sP4cXvt6JYgWDM7N/C3HiSWaIUZkbI888phZ6zc+dJSqE7lDzL42sp3HD4LHq87/ru4caVimLuU569qN8zEt5/ilLofaYuESmFNkD2YRGUQvfhvzRvGz7786C5+1MOngTnyviF6pRC99lazUkptErMWn5KoTVeVnL7WgrXHjiLuz90lcIba4dg+sOcKXSnLx33nkJ3Ku2tPJRCb5F0ZhxKofv9cinhillGXr0/En2vr4zRd9bP8GNO6ZUAACAASURBVGFKoftsreakFFolZi0/pdAaLyu5fSmFR89ewLOzNmL9obMuVR7X6zr0blbRSlMcl5czhTZ0CaXQBsg+LIJSaA3+1uPnjRieibmEMd3r44FWla8ZgFJoja2V3JRCK7Ss56UUWmfm7hO+kkI5bfzsVxux/UQUqpYsgNvql8HB0zHIH5zLvF2h63Vl3W2CY/NRCm3oGkqhDZB9WASl0Dr8ORuOYfA3m5A3d5BZRm5RtXi6QSiF1tm6+wSl0F1SnuWjFHrGzZ2nfCGFYUfPmxnCA6dj0KhiUcx5qjVyZsM72SmF7ozALOahFGYRoMMfpxR61kFvLNqJD37fh+sqFMGM/i1RNH9ul0CUQs/YuvMUpdAdSp7noRR6zi6zJ+2WwjUHzhghDD9/EW1rhmCmn58wzogvpTCz0eeFzymFXoDo4BCUQs87p//0tfh15ylzL7Lcj5w2UQo9Z5vZk5TCzAhl7XNKYdb4ZfS0nVK4bFeEEUJ53+rtDcpi8v1N9BrmgMiUQhs6gVJoA2QfFkEp9Bz+/ogY9J22BrJ5O717QimFnrPN7ElKYWaEsvY5pTBr/JwghT9tDTdCGHf5Cvo0r4g3el6n1yiHRKYU2tARlEIbIPuwCEph1uDLN94nPl9vgsjrHOS1DsmJUpg1thk9TSnUYyuRKYV6fO2YKZy78Rie/3qTacRjbavhxdvr6DXIQZEphTZ0BqXQBsg+LIJSmHX47yzdg/FLdqNGqYLm4Em5ovlMUEph1tleKwKlUI8tpVCXrbYUfrnmMEbM3WIaMfiWWhh0U03dBjkoOqXQhs6gFNoA2YdFUAq9A3/glxuwIOwEujQoi/f/2bdDKfQO2/SiUAr12FIKddlqSuEnfxzAqwu2mwa83K0e+rWuotsYh0WnFNrQIZRCGyD7sAhKoXfgy8m+vtP+wu6Tf+O5TrXwXKeanCn0Dtp0o1AKFeFy+VgVrpYUvvfbXrz18y5Tdyt3tKs21ubglEIbgFMKbYDswyIohd6Dv3x3hBFDSTJb2LZKQQQFBSF//vzeK4SRDAFKoe5A4J5CPb4aUigyKFIo6aO+zXBL3dJ6DXBwZEqhDZ1DKbQBsg+LoBR6F/7UFfsxZuEO897CVlWKoniBYLSpVdq8DoLJewQohd5jmV4kSqEeX29I4cmoi4iOu4wKxfJj3E87IcvGkmYNaGXuZg/URCm0oecphTZA9mERlELvw+/49u/YFxF9VeBht4XiyRure7+wAI1IKdTteEqhHt+sSGHClUQMmLEOS3eeMhWUW0muJCaaPy8c1Bb1yhXWq7gfRKYU2tBJlEIbIPuwCEqhd+HHJ1xBzRcXuQStHlIQS/+vvXcLC+BolELdzqcU6vHNihQmv+kgbe0CfYYwmQelUG/cpkSmFNoA2YdFUAq9Cz8iOg7Nx/ziErRYgWBsHHWzdwsL4GiUQt3OpxTq8c2KFD4+cz1+3hbuUrlPHmqGjnUCcx9hahiUQr1xSym0ga0TiqAUer8XGrz8M/6+ePmqwLL3549hHbxfWIBGpBTqdjylUI9vVqTwkelrU5aOU9dwxiMt0K7mvy/O16u9syNTCm3oH84U2gDZh0VQCr0Pf8qyfXjzp50ugSf1aYw7G5XzfoEBGJFSqNvplEI9vp5K4fpDZyEzhaej466qXLH8wfjzhZuQN3eQXqX9JDKl0IaOohTaANmHRVAKdeBvPx6FDQdOIXdQTmw/dQGfrTqIXDlz4MO+zdAxtJROoQEUlVKo29mUQj2+nkjhku0nMfTbzTh3IR4Vi+c3bzWIuhCP6qUK4vF21dC8SnG9CvtRZEqhDZ1FKbQBsg+LoBTqwU99o8l/523DjD8PmlfVfNy3Gb+JZxE7pTCLADN5nFKox9eqFH699giGzQ4zFbqjYTm8e29jvcr5eWRKoQ0dSCm0AbIPi6AU6sFPe83doFkb8cOm46hQLB9mDbje/M7kGQFKoWfc3H2KUuguKev5rEjh+8v2mfcQSnq0bTWMvL2O9QID6AlKoQ2dTSm0AbIPi6AU6sFP7+5jufFEbj4JLVsYC5+5AUE5c+hVIBtHphTqdi6lUI+vu1I4ZuF2TF2R9FJqkUGRQqaMCVAKbRghlEIbIPuwCEqhHvz0pFBK6/beHwg7eh7NqhTHd09cr1eBbByZUqjbuZRCPb6ZSaG8jHrIt5sxZ8MxUwlZLpZlY6bMCVAKM2eU5RyUwiwjdHQASqFe91xLCs9fiMcd7/6Bw2di0aF2KXz6cHO9SmTTyJRC3Y6lFOrxzUgKI/6Ow9DvwrBs1ynkCw7CjP4tuP/YQldQCi3A8jQrpdBTcv7xHKVQr5+uJYVS4oHTMbhz8kpzgpCbx633AaXQOjMrT1AKrdCylvdaUrgr/G/857swbD56DpWK58cXj7Y0J42Z3CdAKXSflcc5KYUeo/OLBymFet2UkRRKqfLesZ5TVpkK3NuiEl7v0UCvMtksMqVQt0MphXp805PCP/dF4j+zw3DkTCyaVCoGubYuOFdOvUpk08iUQhs6llJoA2QfFkEp1IOfmRRKyYu3nzQX3Et65qYa+L9bautVKBtFphTqdialUI9vWilcGHbCCGFM3GXcUrc0PurbTK/wbB6ZUmhDB1MKbYDswyIohXrw3ZFCKX3W2iMY/s97yF67qwHua1lJr1LZJDKlULcjKYV6fFNL4cw/D2HUvK2msPtaVMJrXC3IEnhKYZbwufcwpdA9Tv6ai1Ko13PuSqHUIPX7yD7t1xwdeOtJhh1DKdQbtxKZUuh9vrGXEvDer3uw6fAZ5MudC4k5cuDXnadMQYM61sTgm2t5v9AAi0gptKHDKYU2QPZhEZRCPfhWpFBqkfq9ZD8929a8y5ApfQKUQt2RQSn0Pt/kd5SmjTz6znroe30V7xcYgBEphTZ0OqXQBsg+LIJSqAffqhRKTQZ/synl/WSbXroFRfPl1qugH0emFOp2HqXQu3zDz19Eq9eXugStXCI/fh/awbuFBXA0SqENnU8ptAGyD4ugFOrB90QKpTb9Pv0Ly3ZFIE/uIIzuVg/nYuNRvlg+dL2urF5l/SwypVC3wyiF3uW7LyIaHd/+3SVo1ZIF8NuQG71bWABHC2gpTEhIgHxjzJcv/ftTr1y5AvmhVLBgQQQFBaUME3lOwBUoUMCtoUMpdAuT32aiFOp1nadSKDW6deJyyHvLUqfW1Uviy8da6lXYjyJTCnU7i1LoXb6frTqIl37Y5hL01npl8OGDTb1bWABHC0gpPHv2LMaNG4dFixaZrm/WrBleeOEFVK9e3fxdPn/ppZewfPlyFC9eHAMHDkSPHj3MZ5MnT8bEiRONEDZv3jzlzxmNIUph9v4XRinU69+sSOH4JbvxztI9LpWTGw7a1QrRq7SfRKYU6nYUpdA7fOMTrmDMgh347M+DLgHLFMmLDx5oikYVi3qnMEYxE15xcXEoUqSIKo0ciYmJiaolWAh+7tw5zJ49G/fddx+Cg4ONIMrX3nzzTROlZ8+eaN26NZ577rmrZgjDwsIwYMAAzJs3DyVLlsSQIUNQsWJFDB48OMPSKYUWOscPs1IK9TotK1I49LvN+HbdUZfK/a9XQ9zdrIJepf0kMqVQt6MohVnnu/1EFMYs2I5V+yJRrEAwRt1eFzfULIlN+8NRIF8etKlVJuuFMMJVBAJSCtOOgVWrVuHVV181M4dr167FsGHDsGTJkquEUJ6ZNGkSoqKiMGrUKBNi/fr1RhxXrFhBKQzgf1iUQr3Oz4oUjvtpp3lNTdr0/v1N0KUB9xZSCvXGrUSmFGaN77xNx83bBOQu4xZVi2NU17poUD5p9iqju4+zViqfphQCZqbw8uXLGDFiBD777DNs374dMrsnv3fs2BGdOnVCnjx5zOehoaHo27evGTnyj75NmzbYuXNnikDKtGvaVL9+fezevdtnoy0+Ph7R0dEoVqyYz+qQnQuOjIxE0aJFXf4TkZ3bbFfbZNzKft5r7fvNqB6yn7D7+6twMT7BJdsieV1NmUJ2NcOR5YgUxsbGmrHL5H0CERERZkUpR44c3g+ezSO+vXg33vttr2nl/S0rYeTtdZA397/7+mVyRlb58ubNm81J2N88kUL53lC4sGev83J3vDtq+Tg1ZpkZfOaZZ/D999+jTJkyRhA//vhjPP/886hRowY+/fRTNGjQwAih7C1s164devfubULIwGzatCk2bdqUcuika9euLr24a9curFy50v7eTVWirN6721k+ragfFk62ep2WVbZHzl3Eb3vO4vzFyyhXOA+2hcdgwbbTpsLjutXAjTUC+z9KWeWr1/P+H5lsrffhiag4TFx2BL/tPYugnDnwfPuK6N24tEsgsrXO1soTWeFbqlQpt4pypBTu27fP7B+cOnWqOWwi6bXXXjOzavK7JJkF7Nevn5G6l19+2RxGkb9LCg8PR9u2bSHSlzPntS/e5p5Ct8aI32bi8rFe12Vl+fhatfrw9314fdFO8/GILnUwoF01vQY4ODKXj3U7h8vH1vj+tuuUOVAir56Rl86Pur0O2tQomW4QLh9bY2sld8AuHx87dswIocwAduvWLYWZzAzu2bMnRQqPHDmCO+64w+w1FHk8ceIERo8ebfKvXr0aQ4cO5Z5CKyMuG+alFOp1qoYUSm2XbD+Jx2asMxW/v1VljO1eX68RDo1MKdTtGEqh+3w/Wr4fr/24wzxwR8NyZv9gqUJ5rhmAUug+W6s5A1IK5R9rnz590L9/f/Tq1SuFmexREFm86aabMH/+fFSrVg3vvvsu5If+66+/jr1795r8CxcuNEvNgwYNQpUqVYwYZpQ4U2h1WPpXfkqhXn9pSaHUeO+paHQan/Qy3LY1S2LmI4H1/kJKod64lciUwsz5Rl2Mx6sLduDbdUdMZrm7WO4wzixRCjMj5PnnASmF06ZNM5KXNs2cOROtWrXC3Llz8corr5iP27dvj2effdYIoqQZM2Zg/Pjx5s9NmjTBhAkTMn2fD6XQ8wHqD09SCvV6SVMKpdbnLsSjw/+W4WzsJVQqnh9yAKVAnlx6DXJQZEqhbmdQCl35ytLw+dh4lC2aD8fPXTCvm9l45BzKF82HkV3ronN9914xQynUG7sBKYXu4JTbTARO/vz5XbLzRhN3CAZOHkqhXl9rS2FyzXtNWYV1h86av/465EZUK+nebUV6LdePTCnUZUwpvJpvv0/XYtmuUylfzB2UE/Ji6htrh2Dk7XVRo1RBtzuEUug2KssZKYWWkVl/gDOF1pn50xOUQr3esksKpQX/+S4M3/yzjDVrQCu0qlZCr2EOiEwp1O0ESuG/fKetPIDR87e7AJf9g+/e29hyR1AKLSNz+wFKoduoPM9IKfScnT88SSnU6yU7pVBakfpk8jt9GqNbo3J6jfNxZEqhbgdQCv/l+8KcLfjqr8MuwMf1ug69m1W03BGUQsvI3H6AUug2Ks8zUgo9Z+cPT1IK9XrJbimUlvy8LRyPz1xvGvV/t9TGMzfV0GugDyNTCnXhUwr/5fvqgu345I8DLsBlllBmC60mSqFVYu7npxS6z8rjnJRCj9H5xYOUQr1u8oUUSmvWHzqLnlNWmYbd3bQC/nd3Q71G+igypVAXPKXwX773fbwGq/YlvTQ+OeUPzoUVwzqgRIFgyx1BKbSMzO0HKIVuo/I8I6XQc3b+8CSlUK+XfCWF0qJDkbHoPnmlOZlcomAwCuXJjfzBQbgptBSG3Fpbr9E2RaYU6oKmFCbxHfzNJszZcAwhhfKYA1yXEq6gYvH8eOj6Kmha2bMbhSiFemOXUqjHNiUypdAGyD4sglKoB9+XUiitiom7jBZjf0HMpavvT5YlZVla9udEKdTtPUohMOTbzfhu/VHzuqcpDzRFvXKe3aebtqcohXpjl1Kox5ZSaANbJxRBKdTrBV9L4eEzsWg37jeXBtYvXwQLnrlBr+E2RKYU6kIOdClMPs1foVg+I4QNyhfxGnBKoddQugSiFOqxpRTawNYJRVAK9XrB11KY+taT1K0sUzgvVo/oqNdwGyJTCnUhB7IUDp+9BbPWHka5ovkw5f4maFixqFdhUwq9ivOqYJRCPbaUQhvYOqEISqFeL/haCqVlDV9ZjPMX4l0a+eLtdfBY26SbjvwxUQp1ey1QpXDE3C34cs1hlCmS1whh40qe7RvMqHcohXpjl1Kox5ZSaANbJxRBKdTrBSdIoWySH71gG87FJolhtZCC2B8Rbf4sUihy6I+JUqjba4EohSO/34rPVx9CqUJ5zJKxpwdJMusZSmFmhDz/nFLoOTu3n+RBE7dR+WVGSqFetzlBCpNbd+B0DIKDcqJ8sXzYfPQc+k1ba04md2tYDq/3aOB3dyZTCvXGrUQONCn877xtmPHnQZQsmAfv398ELaoWVwNMKVRDa673jYuLQ5Ei3tsDml5tcyQmJibqNcPZkSmFzu6frNaOUphVgtd+3klSmLaWx85dwLNfbTR3JsueqQn3NPKrO5MphXrjNtCk8JX52/DpyoMoXiDYCKH2FZGUQr2xSynUY5sSmVJoA2QfFkEp1IPvZCmUVsddvoLhs8Mwd+MxFM2fGx880FT9B6K3aFMKvUUy/TiBMlOYfFtJkXy5zZJx6+r6d4ZTCvXGLqVQjy2l0Aa2TiiCUqjXC06XwuSWj/1xBz5evt/81V/uTKYU6o3bQJkpHLtwBz5esR+F8uYyQnhDjZK6UP+JTinUw0wp1GNLKbSBrROKoBTq9YK/SKEQ+HD5frz+4w4Dwx9OJlMK9cZtIEjh64t24MPf95u9tHLKuF2tEF2gqaJTCvVQUwr12FIKbWDrhCIohXq94E9SKBTmbDiKwd9sNkCcfjKZUqg3brO7FL75005MWbYP+XIHYcoDTXBj7VK6MNNEpxTq4aYU6rGlFNrA1glFUAr1esHfpFBILN8dgWdnbUo6mdyoHF6/y5knkymFeuM2u0nhXwfOYNvxKATlBLYej8I3a48gT66cZslY7gK3O1EK9YhTCvXYUgptYOuEIiiFer3gj1IoNLYfj8LwOWEIO3reHDx5rUcDx51MphTqjdvsJIWTftmDCb/svgpWUM4c+PCBpuhUt7QuxGtEpxTqYacU6rGlFNrA1glFUAr1esFfpdBIQVScEcNfd54yQihiKK/siI67jIrF8iOkUB49cG5EphS6ASkLWbLL6eN6L/2MmLjLV5GoWDw/VvynQxboZO1RSmHW+GX0NKVQjy2l0Aa2TiiCUqjXC/4shULlSmIi5B7Yb9YdQc4cOczfk9PAm2pgyC219eBlEplSqIs+O0hhZPQlNB2zxAWUvH5p039v0QWYQXRKoR56SqEeW0qhDWydUASlUK8X/F0Kk8n0mrLKvOQ6bfr1/9qba/N8kSiFutSzgxQu3XEKj362FmlvnqhRqiB+GdxeFyCl0Cd8KYU2YOfLq22A7MMiKIV68LOLFA6YuQ6Lt510ATX1oWboVMc3+7IohXrjViL7uxS+9+tevLV4V7qQRnWti0duqKoLkFLoE76UQhuwUwptgOzDIiiFevCzixQ+9/UmfL/xmAuol7vVQ7/WVfQAZhCZUqiL3V+l8PCZWPO+zUVbww0g2eJQNaQAthw9Dzlg0rxKcdxY2753EqbXS1w+1hu7lEI9timRKYU2QPZhEZRCPfjZRQp/2HQcg2ZtdAFVME8ujLi9Du5rUUkP4jUiUwp1kfujFIoIihCKGMoS8YgudXzyypnMeoZSmBkhzz+nFHrOzu0nKYVuo/LLjJRCvW7LLlIohL5eewQ/bjmBqIvxqFayoDl0IncmS+p7fRVzC4q8+82uRCnUJe1vUihLxbJkLKlbw3JGCMsUyasLycPolEIPwbnxGKXQDUhZzUIpzCpBZz9PKdTrn+wkhelRklPJcn/s+QvxaFG1OF7sUgcNKxbVA5oqMqVQF7O/SOGek3/j9UU7zauTJA3vHIon2lfXhZPF6JTCLALM4HFKoR7blMiUQhsg+7AISqEe/OwuhUIu7Og5I4ZrDpxB4Xy5jRje07yiHtR/IlMKdRH7gxTKPlcRwpNRF1GnbGG80DnU1juMPe0BSqGn5DJ/jlKYOaMs56AUZhmhowNQCvW6JxCkUOjFXb6CsQu3Y8afhwzMh9tUMct3ueVeMaVEKVQC+09YJ0uhbF0QGfx4+X5T255NKuCFLqEoWdC3L1R3t0cohe6Ssp6PUmidmeUnKIWWkfnVA5RCve4KFClMJvjFmsNGDmMvJeD6aiXMIZQG5YuoAKYUqmBNCepUKdx67LwRwpV7T5vTxPKfD1++XsaTXqAUekLNvWcohe5xylIuSmGW8Dn+YUqhXhcFmhQKyfWHzprl5A2Hz6JY/mDzQ/vuZhW8DplS6HWkVwV0ghQeORsLOfke8XecOTSSK2dOvPfbHpyLjcd1FYrghc51cH31ErogFKJTChWg/hOSUqjHNiUypdAGyD4sglKoBz8QpVBoyv3IIoZf/XXYwJWZHDmdLFfleStRCr1FMv04vpbCE+cvoMukP3A29pJLBfs0r4gXutRBkXy5dSEoRacUKoEFQCnUY0sptIGtE4qgFOr1QqBKYTLRz1YdxNgfd+DS5StoU6OkOYRSt1xhREbHIW9wEAoE5/IYPqXQY3RuPehrKZy64gDGLNzuUtfujcth4j2N3WqDUzNRCvV6hlKox5ZSaANbJxRBKdTrhUCXQiG7en+kmTXccuw85GXXuYJymOU/SbfWK4N37m3s0fsNKYV641Yi+1oKH5+5Dj+nc7XisNtC8eSNzn7lTGY9QynMjJDnn1MKPWfn9pNcPnYblV9mpBTqdRulMImtSOAr87elvOw6NfHH21cze8OsJkqhVWLW8vtKCudtOo6v1x7Gqn2R6VZ4Yp9G6N6ovLXGOCw3pVCvQyiFemw5U2gDWycUQSnU6wVK4b9s5eBJj/dXucCWl15/8/j1ljuBUmgZmaUH7JbC79YfNbfmrD14xtSzaskCZm+qHDJJTo0rFcXcp9pYaocTM1MK9XoloKUwISEB8o0xX7581yQcFxeH4OBg5Ei1wVueE3AFChRwq2c4U+gWJr/NRCnU6zpK4b9sNx89hzvfW+kCu2j+3JjQuxE6hJay1BGUQku4LGe2QwoTE4FZaw8bGdx05JypY71yhdG7WUXzAvTgXDnN1Yqnoy+hdKE86NygrOV2OPEBSqFerwSkFJ49exbjxo3DokWLDNlmzZrhhRdeQPXqV++zkM8HDRqExYsXo2rVqibv5MmTMXHiRCOEzZs3T/lzRl1EKdQbwE6ITCnU6wVK4dVsW722FOFRF9MFLvfV9mtdBU0qF3OrQyiFbmHyOJOmFMrBo1lrjxgh3H48ytRR+v2eZhXRu3lFeO+MusfNV32QUqiHNyCl8Ny5c5g9ezbuu+8+Mwsogihfe/PNN1NIR0RE4J577sGZM2cwd+5cI4VhYWEYMGAA5s2bh5IlS2LIkCGoWLEiBg8enGEPUQr1BrATIlMK9XqBUng1W7kK752le7D9RBQKBAehQ+1SKJo/GHJKOepi0uGTB6+vbOSwekjBDDuGUqg3biWyN6TwyJlYU8mKxfOb32U5WGYFRQjlzmJJrauXMCLo7/sErfQGpdAKLWt5A1IK0yJatWoVXn311ZSZQ/n88ccfR+fOnfH2229jxowZRgonTZqEqKgojBo1yoRYv349nnvuOaxYsYJSaG3cZavclEK97qQUusd2f0QMpq86iBl/HjQPFMqbCw+1rmLk8FpXl1EK3WPraa6sSKHI//DZYThwOsYUX7lEftxQoyRW7ovEwX++dlNoKbNMfFv9Mp5W0W+foxTqdR2lEDAzhZcvX8aIESMM6Tlz5hhB/Pjjj9GqVSt89dVXRgrl89DQUPTt29fkk3/0bdq0wc6dOxEUFGS+dvhw0stmU6eOHTtix44der2YSWRpW0xMDIoU0bkuy2cNc0jBMstcuHBh5Mypd0+tQ5pqezVk3Mq/rbx589petj8WKPvKZqw+jB82nzDVL180H/peXwl9W1VyuUc5Pj4eFy5cMGOXyfsEZJWpWLFiV+1Hd7eUXh+uSdkjmPaZ2+qVxt1NK6B9rZLuhst2+aKjo80qn/xi8i4B+c+i/CpYMOOVhmuVmiuXe+9OzZGYKFtinZfWrl2LZ555Bt9//z3KlCmDY8eOoWfPnmaJuHTp0ldJ4cCBA9GuXTv07t3bNERmDZs2bYpNmzalHDp55JFHXBq5fPlyrF692meNF/RXrlxJEVefVSSbFizSLeKS+jBSNm2q7c2ScSuJwm0N/cr95/D1xnDI75JqlyqAPk3KoFuDkJRA/L5gjanV3PJ9wd0fkMmx5afkhqN/Y8CsbekWN6V3XbSoTImXw57y/ZbfF6yOyszzy/dc+d6QPNGV+RNX5yhRwr1rEx0phfv27TMCOHXqVHPYRGD069cPrVu3Rq9evUxLu3btag6X1K1bF6+99po5jCJ5JIWHh6Nt27bYtWtXhoOTewqtDiv/ys/lY73+4vJx1tjO23TMLCtvPJwkh7L/TJaUixUIxq87wnE+5iLqVyyJ+1pWylpBfNqFgLvLx3JQZO2hM1h38Kx5UXnqV8ikDponV07sGtOZpAFw+VhvGATs8nHyjKAsCXfr1s0Qlinpxo3Tv/5n7NixiIyMxIkTJzB69GiTX2b/hg4dyj2FeuPTLyJTCvW6iVLoHbay11DkUPYeppc61SmNqQ81805hAR4lJu6yecn4vhORqFSqGO5oWO6qfZ2HImOx7tAZrN4XiVX7I3Hs7IUUYnK39Q01S+Jk1EXsCk86SJKcul5XFu/d1yTA6SY1n1KoNwwCUgrlf3B9+vRB//79U2YEBbHsT0g7HZ16T+HevXtN/oULF5qlZnldTZUqVYwYZpQ4U6g3gJ0QmVKo1wuUQu+xldPJckr53V/3mruU06ZfBrdHjVKe7SPyXi2dEUmWcVO9mtbtSsVdvoLbRVdk/AAAG4ZJREFU31mBvaeiU54pVSgPnu9UC1uPR+HPfaex/5+DIskZ6pQtbA6RNK9SDM2rFDezuLGXEjB24Xas3p/0IupW1YrjxdvrIn9w0t71QE+UQr0REJBSOG3aNLz++usuVGfOnGn2EKZO8vdZs2YZ+ZMkJ5HHjx9v/tykSRNMmDAh0wMclEK9AeyEyJRCvV6gFHqf7R3v/mHuUU6bGlYsipvrlIbckCK/Ai2djo7DiDlb8OuuU7ickIiWVYtjZNe6aFA+8wN6kdFx5gXR3286hinL9mWIrkSBYLStFfKPCBY3J4uZrBGgFFrjZSV3QEqhFUDp5eWNJlklmL2epxTq9Sel0Ptsn521EXI/bkapbJG8/8hhCbSvFYIKxa5965P3a+ibiIO+2ogfNl/NRWZOh3cONcKXLH4pv8ckiaD8PbMkp8AfaFXZLA27I5mZxQv0zymFeiOAUqjHNiUyZwptgOzDIiiFevAphd5n+9eBM7h/6hrEJ/y7hNy9cXl0DC1lDjrIkuW+iH+XP6UGdcsVRsuqIogl0a5WCGTvm9yx++Hy/dh3KhqF8+WG7Hl7rG0171dYMeLfFy9j98m/sevk33h1/nZciE/wqLQCeXJBZgCFy8FI132b/72jLvq3SboViynrBCiFWWd4rQiUQj22lEIb2DqhCEqhXi9QCnXYnjh/Ect2hONcTCwaVCplZrBSp63Hz2PF7tP/SGIkZK9ccgoOyonmVYthw+FzuHDpaon6X6/rcHezipYqfSnhCkRUZZ9jzVIFU27vsBJk8faT+OSP/TgcGYti+YPRo0l5PJpKUCW2iN/u8CQBFBHcfTIax8/9e8jjWuXJie0yRfKiRIE8KFEwGCUK5jECWFL+/M/X8uZO2ut3JTERXd/9I+XqOflapeL5MW9gG1MvJu8QoBR6h2N6USiFemwphTawdUIRlEK9XqAU6rF190YTEarluyPw+54IrNob6TKLmLqGInX3NK+UJEwF81z1u8yipU0bDp/FgBnrIfv5ktOw20Lx5I1X30OfEQURu9Zv/OqSpXP9MkhIhBHB9Gbv5IGgnDlQu3Qh1CpTyJz23XEi6R7h5HRdhSL4YeANljrh8pXE/2/vPICkqLYwfEiLZMlRyTmDgmQkKSI5i1CIkilSEUVykpyzZElSIEmy5KQioQBBeTwVJAsokuOr/1o9b2bZ0LM7p3eG+W/V1rJ09723v9vT8/W5oWUNZh9fuiGZ0yaX9wtnkMTx7S3o61VBQbwzpVCv8SmFemwphQ6w9YciKIV6rUAp1GNrVwpD1wBLqszZ81/58rvfvaocImWWLCLihtfv7f/Pnx4zdZEh3HFI7QLy5OkzMwvX+rn/6Inn34///dvuuD68Czp3uiSSK21iyZU2ifm3+/uhozPRJCwQdtcp9AoidzYEKIV6FwKlUI8tpdABtv5QBKVQrxUohXpsoyqFqNH5m/ek/OidL1TurewpJUfqxHLj7r8TMPD75p1HcuveI70TCSfnfOmTSpvy2UwUENFARAXtpqguSeOeP6XQLm3v96MUes/M7hGUQrukorEfJ5pEA14AHEop1GskSqEe2+hIIWo1Y/c5GbflZ0F3KRImqsxu8UaY8oWxdjcwU9dNFvH3rD3n5MrfD144yX8XfA6RBCFxJWG8OGZ9vgQh1u+45m/8P/7v0l8P5OOFP7yQx7A6BcyM35hKlEI98pRCPbaUQj22jBQ6wNYfiqAU6rUCpVCPbXSlEDXDBJQ/bt0zY+bSJn3F68rO3ferDN3wk8dxFXOnlgUflfAqr6k7/iNTdpx1TYipXyyTjGtU2Ks8fL0zpdDXRP+fH6VQjy2lUI8tpdABtv5QBKVQrxUohXpsfSGFvqjdV4cvmJnOD548NUvfdKyYQ0LixvY6a0QjMas6WYJ4fjGxg1LodRPaPoBSaBuV1ztSCr1G5v0B7D72nlkgHUEp1GstSqEeW3+RQr0zjNmcKYV6/CmFemwphXpsGSl0gK0/FEEp1GsFSqEeW0qhHlvkTCnU40sp1GNLKdRjSyl0gK0/FEEp1GsFSqEeW0qhHltKoS5bSqEeX0qhHltKoQNs/aEISqFeK1AK9dhSCvXYUgp12VIK9fhSCvXYUgo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   ],
   "source": [
    "fig = px.line(x=bends, y=totals, markers=True, width=350, height=250)\n",
    "\n",
    "fig.add_annotation(\n",
    "    x=60, y=350, text=\"3-fold cross-validation\", showarrow=False\n",
    ")\n",
    "\n",
    "fig.update_layout(\n",
    "    showlegend=False, xaxis_title=\"Location of bend\", yaxis_title=\"MSE\"\n",
    ")\n",
    "\n",
    "fig.show()"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The MSE looks quite flat for 57 to 60 degrees. The minimum occurs at 58, so we choose that model. To assess this model on the test set, we first fit the bent line model at 58 degrees on the entire train set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "bent_final = LinearRegression().fit(\n",
    "    X_train.loc[:, [\"temp\", \"temp58p\"]], y_train\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we use the fitted model to predict gas consumption for the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "y_pred_test = bent_final.predict(X_test.loc[:, [\"temp\", \"temp58p\"]])\n",
    "\n",
    "mean_squared_error(y_test, y_pred_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's overlay the bent-line fit on the scatter plot and examine the residuals to get an idea as to the quality of the fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": [
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font-size: 14px; fill: rgb(36, 36, 36); opacity: 1; font-weight: normal; white-space: pre;\">Gas (ft^3)</text></g><g class=\"g-y2title\"/></g></svg>"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "err58 = y_test - y_pred_test\n",
    "\n",
    "temp = np.arange(10, 80, 1)\n",
    "temp58p = (temp - 58) * (temp >= 58)\n",
    "\n",
    "Xs = pd.DataFrame(\n",
    "    data=np.transpose([temp, temp58p]), columns=[\"temp\", \"temp58p\"]\n",
    ")\n",
    "y_hats = bent_final.predict(Xs)\n",
    "\n",
    "\n",
    "fig = make_subplots(rows=1, cols=2)\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=X_test[\"temp\"], y=y_test, mode=\"markers\"), row=1, col=1\n",
    ")\n",
    "\n",
    "fig.add_trace(go.Scatter(x=Xs[\"temp\"], y=y_hats), row=1, col=1)\n",
    "fig.update_xaxes(title=\"Temperature (<sup>o</sup>F)\", row=1, col=1)\n",
    "fig.update_yaxes(title=\"Gas (ft^3)\", row=1, col=1)\n",
    "\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=X_test[\"temp\"], y=err58, mode=\"markers\"), row=1, col=2\n",
    ")\n",
    "\n",
    "fig.add_shape(\n",
    "    type=\"line\",\n",
    "    x0=0, y0=0, x1=80, y1=0,\n",
    "    line=dict(color=\"Black\", width=3),\n",
    "    row=1, col=2,\n",
    ")\n",
    "\n",
    "fig.update_xaxes(title=\"Temperature (<sup>o</sup>F)\", row=1, col=2)\n",
    "\n",
    "fig.update_layout(\n",
    "    height=250, width=550,\n",
    "    showlegend=False,\n",
    "    title={\n",
    "        \"text\": \"Residuals\",\n",
    "        \"y\": 0.9,\n",
    "        \"x\": 0.85,\n",
    "        \"xanchor\": \"right\",\n",
    "        \"yanchor\": \"top\",\n",
    "    },\n",
    ")\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fitted curve looks reasonable, and the residuals are much smaller than those from the polynomial fit.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "\n",
    "For teaching purposes in this section, we use `KFold` to manually split up the training data into three folds, then find the model validation errors using a loop. In practice, we suggest using `sklearn.model_selection.GridSearchCV` with an `sklearn.pipeline.Pipeline` object, which can automatically break the data into training and validation sets and find the model that has the lowest average validation error across the folds.\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using cross-validation to manage model complexity has a couple of critical limitations: typically it requires the complexity to vary discretely; and there may not be a natural way to order the models. \n",
    "Rather than changing the dimensions of a sequence of models, we can fit a large model and apply constraints on the size of the coefficients. This notion is called regularization and is the topic of the next section. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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